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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

On the Effect of Beating during Nonlinear Frequency Chirping

Spectroscopic analyses of energetic particle (EP) driven bursts of MHD fluctuations in magnetically confined plasmas often exhibit chirps that occur simultaneously in groups of two or more. While the superposition of oscillations at multiple frequencies necessarily causes beating in the signal acquired by a localized external probe, self-consistent hybrid simulations of chirping EP modes in a JT-60U tokamak plasma have demonstrated the possibility of global beating, where the mode's electromagnetic field vanishes globally between beats and reappears with opposite phase [Bierwage et al., Nucl. Fusion 57, 016036 (2017)]. This implies that there can be a single coherent field mode that oscillates at multiple frequencies simultaneously when it is resonantly driven by multiple density waves in EP phase space. Conversely, this means that the EP density waves are mutually coupled and interfere with each other via the jointly driven field, a mechanism ignored in some theories of chirping. In this thesis-style treatise, we study the role of field pulsations in general and beating in particular using the Hamiltonian guiding center orbit-following code ORBIT with a reduced wave-particle interaction model in realistic geometry. Beating is found to drive the evolution of EP phase space structures. Additionally, a key mechanism is the pulsation of effective phase space islands combined with the alternation of their effective O- and X-points due to phase jumps between each beat. Observations: (1) Beating causes density wave fronts to advance radially in a pulsed manner and the resulting chirps become staircase-like. (2) The pulsations facilitate convective transfer of material between neighboring layers of phase space density waves. On the one hand, this may inhibit the early detachment of solitary phase space vortices. On the other hand, it facilitates the accumulation of hole and clump fragments into larger structures. (3) Long-range chirping is observed when massive holes or clumps detach and drift away from the turbulent belt around the seed resonance. It is remarkable that the detached vortices remain robust and,on average, maintain their concentric nested layers while being visibly perturbed by the field's continued beating.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Effects of spatiotemporal plasma power distribution on the modeling of ignition kernel evolution in quiescent and turbulent methane/air mixtures

Abstract The present work improves a phenomenological plasma-assisted combustion model by integrating the spatiotemporal distribution of plasma power density, thereby considering the evolution of plasma streamers in the modeling, and subsequently, better predicting the ignition kernel evolution. The improved phenomenological model is validated against experiments representing the plasma discharge and post-discharge ignition kernel evolution. Specifically, the new model demonstrates a more accurate prediction of ultrafast gas heating and O 2 dissociation during the plasma discharge, compared to the original model. In addition, the new model is found to closely match the experimental pressure wave and heated channel profiles post-discharge without the need for tuning the energy deposition (unlike the original model), highlighting its accuracy of post-discharge ignition kernel dynamics. The improved phenomenological model is then employed to investigate ignition kernel evolution for a stoichiometric methane-air discharge across various discharge gap configurations. Simulations reveal a non-uniform temperature and streamer distribution progressing from the electrode tips toward the center, contrasting uniform cylindrical discharges previously described in the original model. Streamer propagation is observed to be faster for larger gaps when maintained at the same average electric field for different discharge gaps. The tendency of smaller gaps to produce detached toroidal ignition kernels is observed, while larger gaps promote cylindrical and attached ignition kernels. Interactions between successive ignition kernels from consecutive discharges varied significantly, with the smallest gap (1 mm) promoting the quenching of the preceding ignition kernel due to the initial kernel–kernel separation. The intermediate gap (2 mm) promotes detached kernel growth. In contrast, in the largest gap (4 mm), kernels consistently combine and expand attached to electrodes. The impact of homogeneous isotropic turbulence is also explored, showing the persistence of ignition kernels early on but eventually quenching due to enhanced radical and heat losses with pronounced turbulence intensity.

Johnson, Praise Noah↗
DOE OSTI2023

A conservative Galerkin solver for the quasilinear diffusion model in magnetized plasmas

We propose a conservative Galerkin scheme for the quasilinear model in three-dimensional momentum space and three-dimensional spectral space, with cylindrical symmetry. We construct an unconditionally conservative weak form and use a discretization that preserves conservation properties independent of the wave emission probability. The discrete operators, combined with a consistent quadrature rule, preserve all the conservation laws rigorously. The proposed scheme is quite general: it works for both relativistic and non-relativistic systems, for both magnetized and unmagnetized plasmas, and even for problems with time-dependent dispersion relations. We represent the particle distribution by continuous basis functions and use discontinuous basis functions for the wave spectral energy density, which enables the application of a positivity-preserving technique. We adopt the marching simplex algorithm, designed initially for computer graphics, for numerical integration on the resonance manifold. Furthermore, the numerical examples with a bump-on-tail initial configuration show how the unstable waves produce strong momentum space diffusion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Planetesimal Impact Vapor Plumes and Nebular Shocks Form Chondritic Mixtures

The origin of chondrules and the chondritic sedimentary rocks that dominate the meteoritic record is a long-standing problem in planetary science. Here, we develop a physical model for the formation of chondritic mixtures as an outcome of vaporizing collisions between planetesimals that were dynamically excited by the growth and migration of planets. We present calculations of nebular shock waves generated by impact vapor plumes and focus on aspects of the plume interaction with the nebular gas and dust that have been neglected in previous studies of impact ejecta. We find that when water dominates the vapor, the plumes are relatively cool. However, the plume expansion is supersonic and can drive strong shock waves in the dusty nebular gas. Portions of these nebular shock fronts initially melt nebular dust, forming chondrules that are coupled to the moving front. As the shock front expands and cools, the chondrules solidify, while the shock front entrains additional dust. Eventually, the plume expansion stalls and then hydrodynamically collapses, turbulently mixing variably processed dust and size-sorted chondrules. For probable impact parameters and nebular conditions during giant planet growth and migration, the impact-generated mixtures have characteristics that span the range observed in chondritic meteorites, providing an environment for rapid formation of chondritic assemblages after chondrule formation. Our impact vapor and nebular shocks model, named the IVANS model, links chondrule formation to the overall context of planet formation and provides a framework for interpreting the detailed chronological and geochemical record contained in chondritic meteorites.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

X-ray phase contrast and absorption imaging for the quantification of transient cavitation in high-speed nozzle flows

In this work, high-flux synchrotron radiation has been employed in a time-resolved manner to characterise the distinct topology features and dynamics of different cavitation regimes arising in a throttle orifice with an abrupt flow-entry contraction. Radiographs obtained though both X-ray phase- contrast and absorption imaging have been captured at 67,890 frames per second. The flow lied in the turbulent regime (Re=35,500), while moderate (CN=2.0) to well-established (CN=6.0) cavitation conditions were examined encompassing the cloud and vortical cavitation regimes with pertinent transient features, such as cloud-cavity shedding. X-ray Phase-Contrast Imaging (XPCI), exploiting the shift in the X-ray wave phase during interactions with matter, offers sharp-refractive index gradients in the interface region. Hence, it is suitable for capturing fine morphological fluctuations of transient cavitation structures. Nevertheless, the technique cannot provide information on the quantity of vapour within the orifice. Such data have been obtained utilising absorption imaging, where beam attenuation is not associated with scattering and refraction events, and hence can be explicitly correlated with the projected vapour thickness in line-of-sight measurements. A combination of the two methods is proposed, as it has been found is capable of quantifying the vapour content arising in the complex nozzle flow, while also faithfully illustrating the dynamics of the highly-transient cavitation features.

42 ENGINEERING↗
DOE OSTI2025

Optimization of simulated high-field side lower hybrid current drive coupling using machine learning predictions of scrape-off layer density

Lower hybrid current drive (LHCD) is a potential source of non-inductive off-axis current drive (CD) for tokamaks. Although LHCD has been successfully deployed on a number of tokamaks, it is highly sensitive to the scrape-off layer (SOL) conditions local to the LHCD launcher. Large gaps between the launcher and plasma core, SOL turbulence, or edge density perturbations due to edge-localized modes can hamper CD or cause large reflected power. These coupling issues in part motivated the installation of an LHCD launcher on the high-field side (HFS) of DIII-D. On the HFS, the SOL is less turbulent and more controllable compared to the low-field side. This quiescence may result in more predictable edge conditions and thus a more predictable CD. Here, in this work, HFS SOL reflectometry measurements are predicted from global plasma parameters using machine learning models. The SOL predictions coupled with the full-wave simulation of the LHCD launcher allow for the prediction of reflected power, directivity, and arcing risk before the discharge. Launcher performance is then optimized using multi-objective Bayesian optimization, finding the shot parameters that result in an optimal SOL density that maximizes CD while minimizing the risk of arcing. The predictions and optimizations of LHCD performance are then accelerated using a surrogate model of the full-wave LHCD simulation.

Bayesian optimization↗
DOE OSTI2022

Study of quasi-collisional effects in laboratory and astrophysical plasmas

High-amplitude turbulence excited in plasmas at small-scales can leave imprint on the radiation produced by (accelerated) plasma particles -- mostly electrons in electron-ion plasmas and both electrons and positrons in lepton pair plasmas. Furthermore, turbulence is known to introduce "effective collisional" effects -- anomalous resistivity, dissipation, diffusion, etc. -- in the otherwise collisionless plasmas. These effective collisions affect radiation transfer and modify optical and magneto-optic effects -- the transmittance and reflectivity coefficients, Faraday rotation, etc. Note that the effective collisions considered in this project are not resonant wave-particle interactions, but much less conventional randomization of particles’ paths. Therefore, we colloquially refer them to as "quasi-collisions". The study of quasi-collisions on transport, radiative and optical properties of plasmas is the main focus of this project.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Fractal Scaling of Explosively Driven Product Gases

ABSTRACT Characterization of the interface between explosive product gases and ambient air in an explosion is a complicated task due to the turbulent mixing and inherently three‐dimensional expansion of the interface. This study aims to quantify the evolution of the interface as a temporally varying Hausdorff dimension. Two test series were conducted with Composition C‐4 charges with masses of 105 and 880 g. Imaging data were collected from the time of detonation until shock wave detachment using ultra‐high‐speed cameras. Gas cloud profiles were extracted using automated image processing algorithms, and the Hausdorff dimension of these two‐dimensional slices of the gas cloud was then estimated using boxcounting algorithms. When scaled with standard gas dynamic nondimensional scalings, the Hausdorff dimension of all explosive events appears to collapse towards a single curve. The fireball was initially nonfractal and began to develop fractal properties as the shock wave separated from the detonation products. Artificial perturbation of the charged surface had no detectable impact on the evolution of the Hausdorff dimension in the early development of the fireball outside of error, despite visible phenomenological differences in the early development of mixing on the fireball surface.

42 ENGINEERING↗
DOE OSTI2021

Intermittent Frontogenesis in the Alboran Sea

Abstract We present a phenomenological description and dynamical analysis of the Alboran fronts using a realistic simulation at submesoscale resolution. The study is focused on east Alboran fronts emerging within relatively strong flows that separate from the Spanish coast into the basin interior. Despite modest lateral shifting associated with the position of the Alboran anticyclonic gyres and variations in intensity, these fronts present a similar structure and dynamical configuration as the climatological Almeria–Oran front. The statistical analysis of our solution shows that strained-induced frontogenesis is a recurrent submesoscale mechanism associated with these fronts, and the process is assessed in terms of the advective Lagrangian frontogenetic tendencies associated with buoyancy and velocity horizontal gradients. Intermittency in their strength and patterns is indicative of high variability in the occurrence of active frontogenesis in association with the secondary (overturning) circulation across the frontal gradient. As a result, we find many episodes with strong surface fronts that do not have much associated downwelling. Frontogenesis and the associated secondary circulation are further explored during two particular frontal events, both showing strong downwelling of (1) cm s −1 extending down into the pycnocline. A frontogenetic contribution of turbulent vertical momentum mixing to the secondary circulation is identified in the easternmost region during the cold season, when the dynamics are strongly influenced by the intrusion of the salty Northern Current. The background vertical velocity fields observed during the analyzed events indicate other currents in the submesoscale range, including tidal and topographic internal waves.

Capó, Esther↗
DOE OSTI2021

Molecular Viscosity and Diffusivity Effects in Transitional and Shock-Driven Mixing Flows

Here, this paper investigates the importance of molecular viscosity and diffusivity for the prediction of transitional and shock-driven mixing flows featuring high and low Reynolds and Mach number regions. Two representative problems are computed with implicit large-eddy simulations using the inviscid Euler equations (EE) and viscous Navier-Stokes equations (NSE): the Taylor-Green vortex at Reynolds number Re = 3000 and initial Mach number Ma = 0.28, and an air- SF 6 -air gas curtain subjected to two shock waves at Ma = 1.2. The primary focus is on differences between NSE and EE predictions due to viscous effects. The outcome of the paper illustrates the advantages of utilizing NSE. In contrast to the EE, where the effective viscosity decreases upon grid refinement, NSE predictions can be assessed for simulations of flows with transition to turbulence at prescribed constant Re. The NSE can achieve better agreement between solutions and reference data, and the results converge upon grid refinement. On the other hand, the EE predictions do not converge with grid refinement, and can only exhibit similarities with the NSE results at coarse grid resolutions. We also investigate the effect of viscous effects on the dynamics of the coherent and turbulent fields, as well as on the mechanisms contributing to the production and diffusion of vorticity. The results show that nominally inviscid calculations can exhibit significantly varying flow dynamics driven by changing effective resolution-dependent Reynolds number, and highlight the role of viscous processes affecting the vorticity field. These tendencies become more pronounced upon grid refinement. The discussion of the results concludes with the assessment of the computational cost of inviscid and viscous computations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

LiDAR Measurements of Wind Shear Exponents and Turbulence Intensity Offshore the Northeast United States

This paper presents wind speed shear exponents and turbulence intensity measurements collected from LiDARs measuring wind speeds from 40m to 200m above sea-level and provides comparisons to industry design guidelines. The high-altitude wind speed data are unique and represent some of the first measurements made offshore in this part of the country, which is actively being developed for offshore wind. The data is used to support the New England Aqua Ventus I Floating Offshore Wind Farm to be located 17km offshore the Northeast United States. Multiple LiDAR measurements were made using a DeepCLiDAR floating buoy and LiDARs located on a nearby island. Here, the measured wind speed shear exponents are compared against industry standard mesoscale model outputs and offshore design codes including the American Bureau of Shipping, American Petroleum Institute, and DNV-GL guides. Significant variation in the vertical wind speed profile occurs throughout the year which is not addressed in design standards. Additionally, turbulence intensity measurements made from the LiDAR, although not widely accepted in the scientific community, are presented and compared against industry guidelines.

42 ENGINEERING↗
DOE OSTI2020

Reconnection from a turbulence perspective

The spectral properties associated with laminar, anti-parallel reconnection are examined using a 2.5D kinetic particle in cell simulation. Both the reconnection rate and the energy spectrum exhibit three distinct phases: an initiation phase where the reconnection rate grows, a quasi-steady phase, and a declining phase where both the reconnection rate and the energy spectrum decrease. During the steady phase, the energy spectrum exhibits approximately a double power law behavior, with a slope near −5/3 at wave numbers smaller than the inverse ion inertial length and a slope steeper than −8/3 for larger wave numbers up to the inverse electron inertial length. This behavior is consistent with a Kolmogorov energy cascade and implies that laminar reconnection may fundamentally be an energy cascade process. Consistent with this idea is the fact that the reconnection rate exhibits a rough correlation with the energy spectrum at wave numbers near the inverse ion inertial length. The 2D spectrum is strongly anisotropic with most energy associated with the wave vector direction normal to the current sheet. Reconnection acts to isotropize the energy spectrum, reducing the Shebalin angle from an initial value of 70° to about 48° (nearly isotropic) by the end of the simulation. The distribution of energy over length scales is further analyzed by dividing the domain into spatial subregions and employing structure functions.

Adhikari, S. (ORCID:0000000321607066)↗
DOE OSTI2025

Turbulent-like flows in quasi two-dimensional dense suspensions of motile colloids

Dense bacterial suspensions exhibit turbulent-like flows at low Reynolds numbers, driven by the activity of the microswimmers. In this study, we develop a model system to examine these dynamics using motile colloids that mimic bacterial locomotion. The colloids are powered by the Quincke instability, which causes them to spontaneously roll in a random-walk pattern when exposed to a square-wave electric field. We experimentally investigate the flow dynamics in dense suspensions of these Quincke random walkers under quasi two-dimensional conditions, where the particle size is comparable to the gap between the electrodes. The results suggest a scaling regime in the energy spectrum ∼k −4 at high wavenumbers, observed consistently across activity levels and particle concentrations. We observe that velocity time correlations decay within a single period of the square-wave field, yet an anti-correlation appears between successive field applications, indicative of a dynamic structural memory of the ensemble.

Luo, Rui [Northwestern Univ., Evanston, IL (United↗
DOE OSTI2025

Design of a correlation reflectometer radiometer diagnostic and measurements of the electron density–temperature cross-phase angle in the H-mode pedestal with small edge localized modes at ASDEX Upgrade

This work presents the hardware design and first results from a newly commissioned correlation reflectometer radiometer diagnostic that measures the cross-phase angle between electron density and temperature fluctuations in ASDEX Upgrade plasmas. This diagnostic employs cross correlations between signals measured by a tunable, continuous wave, perpendicular incidence, fluctuation reflectometer, and a 24-channel radiometer sharing the same line of sight. Novel measurements in the pedestal of a helium H-mode plasma with small edge localized modes show changes in the cross-phase angle between the electron density and temperature fluctuations from ∼90° to 120°, suggesting changes in the properties of the turbulence driving transport in the plasma edge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Quantifying electron cyclotron power deposition broadening in DIII-D and the potential consequences for the ITER EC system

Abstract The injection of electron cyclotron (EC) waves fulfills a number of important tasks in nuclear fusion devices for which detailed knowledge of the spatial power deposition profile is critical. This deposition profile is commonly determined using forward models such as beam or ray tracing. Recent numerical and experimental studies have shown that small-angle scattering of the EC beam as it passes through the turbulent plasma edge can cause significant broadening of the effective deposition profile, leading to considerable underestimation of the deposition width by forward methods. However, traditional inverse methods to determine the deposition profile from measurements overestimate the deposition profile width due to transport broadening. In this work, we implement three novel methods to resolve the EC power deposition profile from measurements that counteract transport broadening by simultaneously resolving transport and power deposition. We validate their assumptions and compare the results from these methods to the traditional break-in-slope method as well as to the TORAY ray-tracing code in a set of DIII-D discharges spanning five different confinement modes. We show that the four different inverse methods, novel and established, paint a consistent picture of deposition broadening. Specifically, we show that the measured power deposition profile is between 1.6 and 3.6 times wider than the TORAY profiles. Moreover, we show the considerable consequences that this level of broadening can have for ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Late-time post-merger modeling of a compact binary: effects of relativity, r-process heating, and treatment of transport

Detectable electromagnetic counterparts to gravitational waves from compact binary mergers can be produced by outflows from the black hole-accretion disk remnant during the first 10 s after the merger. Two-dimensional axisymmetric simulations with effective viscosity remain an efficient and informative way to model this late-time post-merger evolution. In addition to the inherent approximations of axisymmetry and modeling turbulent angular momentum transport by a viscosity, previous simulations often make other simplifications related to the treatment of the equation of state and turbulent transport effects. In this paper, we test the effect of these modeling choices. By evolving with the same viscosity the exact post-merger initial configuration previously evolved in Newtonian viscous hydrodynamics, we find that the Newtonian treatment provides a good estimate of the disk ejecta mass but underestimates the outflow velocity. We find that the inclusion of heavy nuclei causes a notable increase in ejecta mass. An approximate inclusion of r-process effects has a comparatively smaller effect, except for its designed effect on the composition. Diffusion of composition and entropy, modeling turbulent transport effects, has the overall effect of reducing ejecta mass and giving it a speed with lower average and more tightly-peaked distribution. Also, we find significant acceleration of outflow even at distances beyond 10 000 km, so that thermal wind velocities only asymptote beyond this radius and at higher values than often reported.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Adaptive mesh based combustion simulations of direct fuel injection effects in a supersonic cavity flame-holder

Here, we present high-fidelity reacting simulations of a supersonic cavity flame-holder configuration. The focus of this work is on flame stabilization brought about by varying the location of fuel injection in a cavity stabilized supersonic flow of air. Central to our approach is a compressible multi-species reacting flow solver that uses adaptive-mesh-refinement (AMR), enabling the resolution of flame, shock-waves, boundary-layers, and small-scale structures in the computational domain. Our analysis indicates that fuel injection closer to the ramp at the aft end of the cavity allows for greater mixing and lower peak temperatures compared to fuel injection upstream that is closer to the backward facing step of the cavity. This difference is mainly due to greater turbulent fluctuations generated from the shear-layer towards the cavity ramp, thereby enhancing the mixing of fuel and air. A low frequency oscillatory behaviour in heat-release and pressure was also observed for the upstream injection case while a much higher-frequency phenomena was observed in the near-ramp injection case. By identifying the important physical determinants of the combustion processes, this study illustrates a promising pathway to design and optimize direct fuel injection strategies in supersonic cavity flame-holders that can improve flame stability, combustion efficiency, and reduce emissions.

42 ENGINEERING↗
DOE OSTI2021

Tidal Energy Resource Characterization, Velocity and Turbulence Measurements, Processed Data, Cook Inlet, AK, 2021

This submission contains processed datasets from a long-term deployment of 3 moorings and a transect survey of the proposed tidal energy site off the East Forelands in Cook Inlet, AK. The long-term mooring datasets were created from 8 instruments mounted on a Terrasond High Energy Oceanographic Mooring (THEOM) bottom lander and two Mid-Water Mooring (MWM) Stablemoor buoys from 1 July 2021 to 31 August 2021 (60 days). The west-most mooring (MWM1) was deployed at 60.720225 N, 151.436196 W in ~50 m of water. The middle mooring (THEOM) was deployed at 60.720703 N, 151.429500 W in ~52 m of water. The east-most buoy (MWM2) was deployed at 60.720081 N, 151.420896 W in ~50 m of water. Each Stablemoor carried three instruments: 1. A Nortek Vector acoustic Doppler velocimeter (ADV) mounted at the Stablemoor's nose. Data were recorded at 8 Hz on a 5 minute duty cycle every 20 minutes. Data was motion-corrected using the internal IMU and external ADCP bottom-track data and then bin-averaged into 4 minute bins and converted to the Principal (streamwise, cross-stream, vertical) coordinate system. (Note: 30 seconds were trimmed from the beginning and end of each 5 minute duty cycle to account for the filter end-effects from turning on and turning off the IMU.) 2. A down-looking Nortek Signature 1000 kHz acoustic Doppler current profiler (ADCP) mounted in the first Stablemoor instrument well. Data were recorded in 2 Hz with 5-beam burst and bottom-track enabled. Processed data has been averaged into 10 minute bins and converted into the Principal coordinate system. 3. An up-looking Nortek Signature 1000 kHz acoustic Doppler current profiler (ADCP) mounted in the second Stablemoor instrument well. Data were recorded at 4 Hz with 5 beam burst enabled. Processed data has been averaged into 10 minute bins and converted into the Principal coordinate system. Note: the down-facing ADCP on MWM1 failed on July 10th, 2021, only recording 9 days of data. Because ADV motion-correction required bottom track, the ADV from MWM1 also only has 9 days processed. Additionally, only 25 days of data were processed from the MWM2 ADV because it appeared to have been impacted by debris on 7/25. Two instruments were mounted on the THEOM (see MHKDR link further below for THEOM raw data): 4. A Nortek Vector acoustic Doppler velocimeter (ADV). Data were recorded at 8 Hz on a 5 minute duty cycle every 20 minutes. Data was bin-averaged into 5 minute bins, and converted to the Principal coordinate system. 5. A Nortek Signature 500 kHz acoustic Doppler current profiler (ADCP). Data were recorded in 4 Hz in the beam coordinate system from all 5 beams. Processed data has been averaged into 10 minutes bins and converted to the Principal coordinate system.

16 TIDAL AND WAVE POWER↗